Geodesic
Commutators of flows and fields
Archivum mathematicum, Tome 28 (1992) no. 3-4, pp. 229-236 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

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The well known formula $[X,Y]=\tfrac{1}{2}\tfrac{\partial ^2}{\partial t^2}|_0 (^Y_{-t}ø^X_{-t}ø^Y_tø^X_t)$ for vector fields $X$, $Y$ is generalized to arbitrary bracket expressions and arbitrary curves of local diffeomorphisms.
The well known formula $[X,Y]=\tfrac{1}{2}\tfrac{\partial ^2}{\partial t^2}|_0 (^Y_{-t}ø^X_{-t}ø^Y_tø^X_t)$ for vector fields $X$, $Y$ is generalized to arbitrary bracket expressions and arbitrary curves of local diffeomorphisms.
Classification : 37C10, 58F25
Keywords: commutators; flows; vector fields 
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Mauhart, Markus; Michor, Peter W. Commutators of flows and fields. Archivum mathematicum, Tome 28 (1992) no. 3-4, pp. 229-236. http://geodesic.mathdoc.fr/item/ARM_1992_28_3-4_a11/

[FK] Frölicher, A., Kriegl, A.: Linear spaces and differentiation theory. Pure and Applied Mathematics, J. Wiley, Chichester, 1988. | MR

[KMS] Kolář, I., Michor, P. W., Slovák, J.: Natural operators in differential geometry. to appear, Springer-Verlag. | MR

[KMa] Kriegl, A., Michor, P. W.: A convenient setting for real analytic mappings. Acta Mathematica 165 (1990), 105–159. | MR

[KMb] Kriegl, A., Michor, P. W.: Aspects of the theory of infinite dimensional manifolds. Differential Geometry and Applications 1(1) (1991). | MR

[KMc] Kriegl, A., Michor, P. W.: Foundations of Global Analysis. A book in the early stages of preparation.

[KN] Kriegl, A., Nel, L. D.: A convenient setting for holomorphy. Cahiers Top. Géo. Diff. 26 (1985), 273–309. | MR

[M] Mauhart, M.: Iterierte Lie Ableitungen und Integrabilität. Diplomarbeit, Universität Wien, 1990.

[T] Terng, Chu Lian: Natural vector bundles and natural differential operators. American J. of Math. 100 (1978), 775–828. | MR